A woman whose body was found near Perth in Western Australia had suffered "significant injuries consistent with a shark attack", police have said.

It is believed the 60-year-old had been diving northwest of Mindarie, a northern suburb of the city, on Sunday morning local time.

Police Inspector Danny Mulligan said her diving partner, believed to be aged in his 50s, felt "something go past him" when he was in the water.

"When he surfaced he saw a commotion in the water and then another boat (a fishing boat) arrived to pull him out of the water, and then it was noticed that the lady had suffered some severe and fatal injuries," he told the Australian Broadcasting Corporation.

The man was able to get back into his own boat and pull the woman from the water but her wounds proved fatal, Mr Mulligan said.

Three fishermen, who also tried to help the woman, described the shark as being longer than their 5.3m boat.

While the cause of the woman's death has not officially been determined, the state's Department of Fisheries agrees with police that the death could be a shark attack and has sent a boat to investigate and to prepare to trap the animal.

On Friday night, surfer Ben Gerring died, three days after he was attacked by a suspected great white shark at Falcon Beach, about 115km south of Mindarie.

Mr Gerring, 29, had been with a group of surfers when the shark tore off his right leg above the knee.

A 4.2m (14ft) shark was caught on Wednesday near the scene of the attack.

The animal was killed at sea but officials could not confirm it was the same one responsible for Mr Gerring's death.

Shark attacks are rare, with 98 worldwide last year, according to the International Shark Attack Files.